Final answer:
The balance in an account with $600 at a 7% interest rate compounded continuously after 5 years is approximately $851.44 using the formula A = Pe^(rt) for continuous compounding.
Step-by-step explanation:
To calculate the balance in an account with a principal of $600 at a 7% interest rate, compounded continuously, after 5 years, we use the formula for continuous compounding:
A = Pert
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time in years.
In this case:
- P = $600
- r = 0.07 (7% expressed as a decimal)
- t = 5
Therefore, the formula becomes:
A = 600e0.07 × 5
Using a calculator to compute e0.35, we get:
A ≈ 600e0.35 ≈ 600 × 1.4190675 ≈ $851.44
So, the balance after 5 years would be approximately $851.44.